\left\{ \begin{array} { l } { x + y = 1 } \\ { y + z = - 2 } \\ { x + y + z = 2 } \end{array} \right.
Solve for x, y, z
x=4
y=-3
z=1
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x=-y+1
Solve x+y=1 for x.
-y+1+y+z=2
Substitute -y+1 for x in the equation x+y+z=2.
y=-z-2 z=1
Solve the second equation for y and the third equation for z.
y=-1-2
Substitute 1 for z in the equation y=-z-2.
y=-3
Calculate y from y=-1-2.
x=-\left(-3\right)+1
Substitute -3 for y in the equation x=-y+1.
x=4
Calculate x from x=-\left(-3\right)+1.
x=4 y=-3 z=1
The system is now solved.
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